How to assign vertex color to vertex color shader node?
face.material.new(name = 'Skin')



'face' has no material property. And as the material is new, there is no vertex color in its node tree (and no node tree as it is).

You can:

mat = bpy.data.materials.new(name = "Skin")
mat.use_nodes = True #Make so it has a node tree

#Add the vertex color node
vc = mat.node_tree.nodes.new('ShaderNodeVertexColor')
#Assign its layer
vc.layer_name = "skin"


Now to link the vertex color output to the default principled shader:

#Get the shader
bsdf = mat.node_tree.nodes["Principled BSDF"]
#Link the vertex color to the shader
mat.node_tree.links.new( vc.outputs[0], bsdf.inputs[0] )


Additionnaly, if you want to add it to the 'face' object:

face.data.materials.append(mat)